Introduction to symplectic topology
著者
書誌事項
Introduction to symplectic topology
（Oxford mathematical monographs）
Clarendon, 1995
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注記
Bibliography: p. [400]-410
Includes index
内容説明・目次
内容説明
Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behaviour of a wide range of physical systems. Over the years, much detailed knowledge has accumulated about the behaviour of particular systems, but the modern global theory of symplectic topology has just emerged. Powerful new methods in analysis and topology have led to a series of striking results, such as Gromov's flexibility theorem on the existence of symplectic structures, and the various proofs of the Arnold conjectures on the number of fixed points of a symplectic map. This book contains an introduction to the subject, which will acquaint the reader with new methods in the field and provide proofs of the simpler versions of the most important new theorems, such as a finite dimensional variational analysis of Hofer-Zehnder.
目次
- From classical to modern
- Linear symplectic geometry
- Symplectic manifolds
- Almost complex structures
- Symplectomorphisms
- Symplectic reductions
- Constructions of symplectic manifolds
- Existence and uniqueness
- Area-preserving diffeomorphisms
- Generating functions
- The Arnold conjecture
- Symplectic invariants.
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